Peel and dice the potatoes, then boil until very soft, about 10 minutes. Drain and mash until smooth, set aside.
In a large bowl, combine the wheat flour and a pinch of salt. Add a tablespoon of oil and rub it into the flour with your fingertips until the mixture resembles coarse crumbs.
Gradually pour in cold water, a little at a time, mixing with your hand or a spoon until the dough comes together into a soft, pliable ball. Knead gently for a couple of minutes, then cover with a damp cloth and let rest for 15 minutes.
Divide the rested dough into 8 equal portions. Roll each into a smooth ball, then flatten slightly.
Using a rolling pin, roll each dough ball into a thin circle about 15cm (6 inches) in diameter. Lightly dust with flour if sticking.
Place a generous spoonful of mashed potatoes in the center of each circle. Optionally, sprinkle with spices like turmeric or chili powder for extra flavor.
Gather the edges and pinch to seal, then gently flatten again and lightly roll to maintain a round shape.
Heat enough oil in a deep pan or wok to reach about 180°C (350°F). To test if hot enough, drop a small piece of dough—if it bubbles and rises immediately, you're ready.
Carefully slide a puri into the hot oil. It should crackle and begin to puff up within seconds. Fry until golden brown, about 30-40 seconds per side, flipping as needed with tongs or a slotted spoon.
Remove the puri with a slotted spoon and drain on paper towels. Repeat with remaining dough balls, adjusting the heat to keep oil steady.
Serve the hot puris immediately alongside the warm, spiced mashed potatoes. Enjoy the crispy, puffy texture and comforting flavors!